Subgroups — C₂×D₁₇×C₁₈₁⋊C₃ #49147355

Order 36924.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₇×C₁₈₁⋊C₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₇×C₁₈₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₇×C₁₈₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₇×C₁₈₁⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₇×C₁₈₁	C₂×C₃	1	1	yes	characteristic, complemented
6	D₁₇×C₁₈₁	C₂×C₃	1	2	yes	complemented
7	C₁₇×C₁₈₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₁₈₁⋊C₃	—	17	1	no	maximal, Hall
9	C₂×C₁₈₁⋊C₃	—	17	2	no	—
10	C₂×C₁₈₁⋊C₃	D₁₇	1	1	yes	characteristic, direct product factor
11	C₂²×C₁₈₁	—	17	1	no	Hall
12	C₁₈₁⋊C₃	C₂×D₁₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₁₈₁	—	17	2	no	—
14	C₂×C₁₈₁	C₃×D₁₇	1	1	yes	characteristic, complemented
15	C₂×C₃×D₁₇	—	181	1	no	maximal, Hall
16	C₁₈₁	C₂×C₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃×C₁₇	—	181	1	no	—
18	C₃×D₁₇	—	181	2	no	—
19	C₂×D₁₇	C₁₈₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₁₇	—	181	1	no	Hall
21	C₂×C₁₇	C₂×C₁₈₁⋊C₃	1	1	yes	characteristic, complemented
22	D₁₇	C₂×C₁₈₁⋊C₃	1	2	yes	direct product factor
23	C₁₇	C₂²×C₁₈₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	3077	1	no	Hall
25	C₂×C₃	—	3077	2	no	—
26	C₂×C₃	—	181	1	no	—
27	C₂²	—	17	1	no	Sylow
28	C₃	—	181	1	no	Sylow
29	C₂	—	17	2	no	—
30	C₂	D₁₇×C₁₈₁⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₁₇×C₁₈₁⋊C₃
commutator, cosocle, hypocenter	C₁₇×C₁₈₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₇×C₁₈₁	C₂×C₃
LCS	G ▷ C₁₇×C₁₈₁
UCS	C₁ ◁ C₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. D₁₇×C₁₈₁⋊C₃	C₂	direct (N × H)
2. C₂×C₁₇×C₁₈₁⋊C₃	C₂	semidirect
3. C₂×D₁₇×C₁₈₁	C₃	semidirect
4. C₁₇×C₁₈₁⋊C₃	C₂²	semidirect
5. C₂×C₁₇×C₁₈₁	C₂×C₃	semidirect
6. D₁₇×C₁₈₁	C₂×C₃	semidirect
7. C₁₇×C₁₈₁	C₂²×C₃	semidirect
10. C₂×C₁₈₁⋊C₃	D₁₇	direct (N × H)
12. C₁₈₁⋊C₃	C₂×D₁₇	direct (N × H)
14. C₂×C₁₈₁	C₃×D₁₇	semidirect
16. C₁₈₁	C₂×C₃×D₁₇	semidirect
19. C₂×D₁₇	C₁₈₁⋊C₃	direct (N × H)
21. C₂×C₁₇	C₂×C₁₈₁⋊C₃	semidirect
22. D₁₇	C₂×C₁₈₁⋊C₃	direct (N × H)
23. C₁₇	C₂²×C₁₈₁⋊C₃	semidirect
30. C₂	D₁₇×C₁₈₁⋊C₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₁₇×C₁₈₁⋊C₃	2
C₂×C₁₇×C₁₈₁⋊C₃	2
C₂×D₁₇×C₁₈₁	3
C₂²×C₁₈₁⋊C₃	17
C₂×C₃×D₁₇	181

Subgroups — C2×D17×C181⋊C3 #49147355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₇×C₁₈₁⋊C₃ #49147355